There are two different types of design employed in the construction of vortex shedding flowmeters. In the first type, the vortex shedding flowmeter has a vortex generator-sensor comprising a vortex generating bluff body of elongated cylindrical shape disposed across the flow passage and a vortex sensing device built into the bluff body, while in the second type, the vortex shedding flowmeter has a vortex generating bluff body and a vortex sensor respectively disposed across two different cross sections of the flow passage in a structurally independent arrangement. While the first type of design provides a structurally compact flowmeter, the second type of design provides a vortex flowmeter with greater sensitivity and reliabilty. For example, a state of the art version of the vortex shedding flowmeter employing the second type design operates in a range of turn-down ratio (the ratio of the maximum to minimum measurable velocities of the fluid) approaching 100 to 1, while the best of the first type of design yields a turn-down ratio of 15-20 to 1 at most. The present invention teaches how to improve the sensitivity of the vortex shedding flowmeter with a vortex sensor-generator of a structurally integral construction and increase the turn-down ratio thereof.